Answer:
f(x) = x³ - 2x² - 19x + 20
Step-by-step explanation:
Given a polynomial with zeros x = a, x = b then the corresponding factors are
(x - a)(x - b) and the polynomial is then the product of the factors
Given zeros x = 5, x = - 4, x = 1 , then
(x - 5), (x + 4) and (x - 1) are the factors, then
f(x) = (x - 5)(x + 4)(x - 1) ← expand the first pair of factors using FOIL
= (x² - x - 20)(x - 1) ← distribute
= x³ - x² - 20x - x² + x + 20 ← collect like terms
= x³ - 2x² - 19x + 20
what's x + y
[tex] {x}^{2} + {y}^{2} + 2xy = 9[/tex]
Answer:
the awnser is 10 and 1/x+ 1/y is = 5/12
After a bicycle tire has done 10 rotations, it has traveled 879.2 inches. Write and solve an equation to find the radius of the tire.
Answer:
14in approx
Step-by-step explanation:
Given data
number of rotations= 10
Distance travelled= 879.2 inches
Hence if in 10 rotations the distance covered is 879.2 inches
in 1 rotation the distance covered will be x inches
cross multiply
10x= 879.2
x= 879.2/10
x= 87.92 inches
This means that the circumference of the tire is 87.92 in
From
C= 2πr
Let us solve for r
87.92=2*3.142*r
87.92=6.284r
r= 87.92/6.284
r= 13.9
Hence the radius is 14in approx
What is the solution to this equation?
Answer:
D
Step-by-step explanation:
Using the rules of logarithms
log x - log y = log ([tex]\frac{x}{y}[/tex] )
log [tex]x^{n}[/tex] = nlog x
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
Given
[tex]log_{3}[/tex] (4x) - 2[tex]log_{3}[/tex] x = 2
[tex]log_{3}[/tex] (4x) - [tex]log_{3}[/tex] x² = 2
[tex]log_{3}[/tex] ([tex]\frac{4x}{x^2}[/tex] ) = 2
[tex]log_{3}[/tex] ([tex]\frac{4}{x}[/tex] ) = 2
[tex]\frac{4}{x}[/tex] = 3² = 9 ( multiply both sides by x )
4 = 9x ( divide both sides by 9 )
[tex]\frac{4}{9}[/tex] = x → D
Solve. 2(2z – 4) = 4
Answer:
[tex]z = 3[/tex]
Step-by-step explanation:
1) Divide both sides by 2.
[tex]2z - 4 = \frac{4}{2} [/tex]
2) Simplify 4/2 to 2.
[tex]2z - 4 = 2[/tex]
3) Add 4 to both sides.
[tex]2z = 2 + 4[/tex]
4) Simplify 2 + 4 to 6.
[tex]2z = 6[/tex]
5) Divide both sides by 2.
[tex]z = \frac{6}{2} [/tex]
6) Simplify 6/2 to 3.
[tex]z = 3[/tex]
therefor, the answer is z = 3.
Vertical, Complementary and Linear Pair Angles Last one maybe?!
Type your answer in the box provided. Make sure to use complete sentences.
Real World: Choose ONE of the following quadratic equations to solve. State your method of solving, giving your reasoning for why you chose that method. Show all work, and put your final answers in context.
A person walking across a bridge accidentally drops an orange into the river below from a height of 140 ft. The equation 0=−x2+7x+18 gives the relationship between how many seconds, x, have passed when the orange hits the water. In how many seconds will the orange hit the water?
A bird drops a stick to the ground from a height of 80 feet. The equation 0=−16x2+64x+80 gives the number of seconds that have passed when it hits the ground. After about how many seconds did the stick hit the ground?
Things you MUST include: (1 point each for a total of 5 points)
Method of solving the quadratic.
Reasoning for choosing this method.
All work to solve the quadratic equation.
The two mathematical answers to the equation.
The answer to the question asked, based on which answer is reasonable.
You may either type your answer in the text box below OR upload a file, picture, or scan of handwritten answers. All files should be saved using the following template: "Last Name_First Name_Assignment Name_Question Number." Refer to Orientation for help with file uploads.
Answer:
A bird drops a stick to the ground from a height of 80 feet. The equation 0=−16x2+64x+80 gives the number of seconds that have passed when it hits the ground. After about how many seconds did the stick hit the ground?
Step-by-step explanation:
h = -16t^2 + 80 Stick hits the ground when h = 0:
0 = -16t^2 + 80
16t^2 = 80
t^2 = 80/16 = 5
t = POSITIVE root 5 (due to the real world nature of the problem)
t approximately 2.236 seconds.
========================================
Graph is a downward opening parabola with h-intercept of 80, t-intercept(s) of sqrt(5), - sqrt(5)
Symmetric about h-axis, though I would only graph on the right side of the h-axis since
that is where t >= 0.
what is the slope of the line through (6, 3) (7, -4)
Answer:
m= -7
Step-by-step explanation:
What is the length of the line?
Answer:
[tex]\sqrt{61}[/tex]
Step-by-step explanation:
x = 6 units horizontally
y = 5 units vertically
Use the pythagorean theorem[tex]\sqrt{x^{2} + y^{2} } = L[/tex]
Plug x and y into the equation, and you will get [tex]\sqrt{61}[/tex] as the length.
Answer:
7.8 units (which is to the nearest tenth)
Step-by-step explanation:
We apply the Pythagorean Theorem here; the length of the line is the length of the hypotenuse of a triangle whose horizontal leg length is 6 and whose vertical leg length is 5 units. This Theorem is expressed symbolically as
a^2 + b^2 = c^2. In this particular case, a = 6, b = 5 and c is to be determined. Performing the calculations, we get
6^2 + 5^2 = c^2, or:
36 + 25 = 61 = c^2
Taking the positive square root of both sides, we get c = √61 ) exactly,
which rounds off to 7.8 units (to the nearest tenth).
The length of the line is 7.8 units.
Find the slope of the line: y+5 = -3/4x
Answer:
y = -3/4x - 5
Slope: -3/4
y-intercept: -5
A rectangle has a length of √7 and a width of 3√8. Find the area of the rectangle.
The area of the rectangle is 3[tex]\sqrt{56}[/tex]
Given,
A rectangle has a length of √7 and a width of 3√8.
We need to find the area of the rectangle.
What is the area of a rectangle?The area is given by:
Area = Length x width
Find the length and width of a rectangle.
Length = [tex]\sqrt{7}[/tex]
Width = 3[tex]\sqrt{8}[/tex]
Find the area of the rectangle.
Area = Length x width
= [tex]\sqrt{7}[/tex] x 3[tex]\sqrt{8}[/tex]
When there are two different square roots we multiply them together under one root.
[tex]\sqrt{a\times b} ~~=~~\sqrt{a}\times\sqrt{b}[/tex]
Now,
= 3[tex]\sqrt{7\times8}[/tex]
= 3[tex]\sqrt{56}[/tex]
Thus the area of the rectangle is 3[tex]\sqrt{56}[/tex]
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Find the slope and y-intercept of the line whose equation is 3x - 5y - 8 = 0
Answer:
[tex]y = \frac{3}{5}x-\frac{8}{5}[/tex]
Step-by-step explanation:
3x - 5y - 8 = 0
-5y = -3x + 8
Divide the whole equation by (-5)
[tex]\frac{-5y}{-5}=\frac{-3x}{5}+\frac{8}{-5}\\\\y = \frac{3}{5}x-\frac{8}{5}[/tex]
PLEASE HELP ASAP PLS AND TY
Find the sum of – 52 , -36 , 42, 8 ,-22 and 46
If the image of point J under a 180° rotation about the origin is (-8, 4), what are the coordinates of point J' ?
help me plzzzzzzzzzz
Answer:
24%
Step-by-step explanation:
Q: Maya has 200 songs on her mobile device. Of these songs, 48 are jazz songs. What percent of Maya's songs are jazz songs?
To find the percentage of something, we can take the number that we want to find the percentage for divided by the total number of items.
In this problem, the number that we want to find the percentage for are the jazz songs, which is 48.
The total number of items is 200 songs.
Therefore, we can divide the number of jazz songs by the total number of songs in order to find the percentage of Maya's jazz songs.
# jazz songs/total # songs 48/200 = 0.24To convert a decimal to a percentage, we can move the decimal point two places to the right (aka multiply by 100).
0.24 → 24%24% of Maya's songs are jazz songs.
give me two numbers that both add to negative 12 and multiply to 11
Answer:
- 1 and -11
Step-by-step explanation:
-1 × -11 = 11
- 1 + - 11 = -12
Brookwood High School is considering adding co-ed soccer to the sports program for the fall season. In order to get an unbiased sample of interest in soccer, who should the school survey?
A.
members of the soccer team
B.
students in freshman homerooms
C.
girls in PE class
D.
every fifth student entering the cafeteria
In order to get an unbiased sample of interest in soccer, the school survey should be conducted D. every fifth student entering the cafeteria.
What are Sampling Methods?Sampling methods are methods used to select a sample using specific methods. This includes various types of probability sampling and non probability sampling methods.
Given that,
Brookwood High School is considering adding co-ed soccer to the sports program for the fall season.
We need to get an unbiased sample of interest.
If the survey is conducted only among the members of the soccer team, the result will be biases because only the interest of someone in the team is known.
Similarly, in the case of students in freshman homerooms and girls in PE class.
If we select every fifth student entering the cafeteria, there is a chance for all the levels of students to be included which eliminates the possible bias.
Hence the option is D.
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PLEASE HELPPPPPPPPP ASAPPPP
Answer:
x = 7
Step-by-step explanation:
Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.
Answer:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
Step-by-step explanation:
Given
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex] -- Missing from the question
Required
The behavior of the function around its vertical asymptote at [tex]x = -2[/tex]
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex]
Expand the numerator
[tex]p(x) = \frac{x^2 + x -3x - 3}{x+2}[/tex]
Factorize
[tex]p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}[/tex]
Factor out x + 1
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)
We are only interested in the sign of the result
----------------------------------------------------------------------------------------------------------
As x approaches -2 implies that:
[tex]x -> -2^{-}[/tex] Say x = -3
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
[tex]p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12[/tex]
We have a negative value (-12); This will be called negative infinity
This implies that as x approaches -2, p(x) approaches negative infinity
[tex]x->-2^{-}, p(x)->-\infty[/tex]
Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)
As x leaves -2 implies that: [tex]x>-2[/tex]
Say x = -2.1
[tex]p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1[/tex]
We have a negative value (-56.1); This will be called negative infinity
This implies that as x leaves -2, p(x) approaches negative infinity
[tex]x->-2^{+}, p(x)->-\infty[/tex]
So, the behavior is:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
inter quartile range 20, 10 , 30 ,40 help please
Answer:
The interquartile range is 30
Step-by-step explanation:
Here, we want to get the interquartile range
We start by arranging the numbers in order
10,20,30,40
The first quartile is;
(n + 1)/4 th term = (4+ 1)/4 = 5/4 = 1.25
This is approximately the first term = 10
Q3 is the third quartile
That is;
3(n + 1)/4 = 3(5)/4 = 15/4 =3.75
This is approximately the 4th term = 40
The interquartile range is the difference between the first and third quartile
Mathematically, we have that as;
40 - 10 = 30
Write 200 as a product of primes.
Use index notation when giving your answer.
Answer:
Step-by-step explanation:
The prime factorization of 200 is as follows: 200 = 2 × 2 × 2 × 5 × 5.
The prime factorization of 200 will be equal to 2 × 2 × 2 × 5 × 5 or 2³ × 5².
It is given that a number is 200.
We have to find out the prime factorization of 200.
What do you mean by prime factorization ?
Prime factorization is a way to find the prime factors of a number, such that the original number is evenly divisible by the prime numbers.
As per the question ;
The given number is 200.
We have to find the prime factors of 200.
This meant to find out the prime numbers we should multiply together to make the original number which is 200.
So ;
200
= 2 × 100
= 2 × 2 × 50
= 2 × 2 × 5 × 10
= 2 × 2 × 2 × 5 × 5
or
= 2³ × 5²
Thus , the prime factorization of 200 will be equal to 2 × 2 × 2 × 5 × 5 or 2³ × 5².
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What is the solution to the inequality below? -1x + 5 < 20
Answer:
x < -15
Step-by-step explanation:
-1x + 5 < 20
- 5 - 5
-1x < 15
/-1 /-1
x < -15
Answer:
x>-15
Step-by-step explanation:
subtract 5 on both sides: -1x<15. Then, divide both sides by (dividing or multiplying by a negative means you have to flip the inequality sign): x>-15.
y =square root 1-x/1+x find it's derivative
Answer:
The first derivative of [tex]y = \sqrt{\frac{1-x}{1+x} }[/tex] is [tex]y' = -\frac{1}{(1-x)\cdot (1+x)^{3/2}}[/tex].
Step-by-step explanation:
Let [tex]y = \sqrt{\frac{1-x}{1+x} }[/tex]. we can determine its first derivative by Rule for the Square Root Function, Rule for Power Function, Rule of Chain and Rule for the Addition of Functions, Rule for the Subtraction of Functions, Rule for the Division of Functions:
[tex]y' = \frac{1}{2\cdot \sqrt{\frac{1-x}{1+x} }}\cdot \frac{(-1)\cdot (1+x)-(1)\cdot (1-x)}{(1+x)^{2}}[/tex]
[tex]y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} }\cdot \left[\frac{-1-x-1+x}{(1+x)^{2}} \right][/tex]
[tex]y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} } \cdot \left[-\frac{2}{(1+x)^{2}} \right][/tex]
[tex]y' = -\frac{1}{(1-x)\cdot (1+x)^{3/2}}[/tex]
The first derivative of [tex]y = \sqrt{\frac{1-x}{1+x} }[/tex] is [tex]y' = -\frac{1}{(1-x)\cdot (1+x)^{3/2}}[/tex].
Will Mark Branliest for Best Answer!! Plz Help!
A juggler throws a ball from an initial height of 4 feet with an initial velocity of 30 feet per second. The height h (in feet) of the ball can be modeled by h=−16t2+vt+s where t is the time (in seconds) the ball has been in the air. v is the initial velocity and s is the initial height.
Write an equation that gives the height (in feet of the ball since it left the juggler's hand. )
Answer:h=16+2+vt +s
Step-by-step explanation:
Please help me anyone ;-;
Answer:
hi
Step-by-step explanation:
Answer:
Part A: two lines, one line will be across $72 all the way. the second line will be a slope.
part b: 5 or less
Step-by-step explanation:
part A: time is x in the equation y=12x and y is the cost. so, plug in the x values and see what y values are. then plot the points and then draw a straight line.
part b: the rider charges $72 dollars for the whole day. if you wanted a bike from bikerama for 6 hours, it would be the same price. so, go for less hours and the price will be better
The nth term of a sequence is 1 - 5n
Work out the 6th term of the sequence.
6th term =
Step-by-step explanation:
nth term = 1 - 5n
6th term = 1 - 5(6)
= 1 - 30
= - 29
PLEASE HELP ME WITH THIS I WILL GIVE BRAINLIEST
Answer:
c
Step-by-step explanation:
Helpp plz I will mark brainliestttt
Answer:
The answer is b
Step-by-step explanation:
The formula for the surface area of rectangular prisms is
A=2(wl+hl+hw)
Now input the length width and hight into the right spots
=2*(2*6.6+3.3*6.6+3.3*2)
And you will end up with the answer
=83.16
Please help, I only have 1 attempt left to get it right, there is also no need to show your work if you don't want to.
How many pounds of $1.75/lb trail mix should a grocer combine with 3 lb of $3.75/lb trail mix to get $2.95/lb trail mix?
Answer:
1/2 lb
Step-by-step explanation:
(1)1.75 + 3(3.75) - 4 = 23.5/4
23.5x/4 = 2.95
23.5x = 11.8
x = 0.5
Answer:
2lb
I don't know what to write here but this is the answer
19 – 5x = 9(1+x) solve
[tex]\Large\boxed{\tt Answer:~x=\frac{5}{7} }[/tex]
[tex]\tt Step-by-step~explanation:[/tex]
Remember: PEMDAS - Parentheses, exponents, multiply/divide, add/subtract
Distribute: 9(1+x) = 9+9x
19 - 5x = 9 + 9x
Add 5x to both sides of the equation and subtract 9 from both sides.
19 - 5x + (5x) = 9 + 9x + (5x)
19 - (9) = 9 - (9) + 14x
10 = 14x
Divide both sides by 14 to get the variable on its own.
10/14 = 14x/14
10/14=x
5/7 = x